All sets of results converge to similar regions of the parameter space about the true parameters, and the spread of uncertainty is quantified similarly in both EKI-GP and B-GP. Table REF  shows the standard deviations of the individual parameters alongside the empirical standard deviation calculated from the ensemble spread in EKI iteration 9. The standard deviations from the MCMC posterior based on EKI-GP and B-GP are similar. We re-emphasize
that the EKI is constructed as an ensemble optimization method and has the property that the ensemble
evolves towards consensus among the parameters, while
also matching the data: the ensemble collapses. As a result, the EKI ensemble spread is an inadequate estimate the uncertainty, as
seen in Table REF .
As explained in the introduction, ensemble methods are only justifiable to quantify uncertainties in the Gaussian posterior setting [1]}, [2]}.
Our approach is justifiable whenever
the GP accurately approximates the
forward model [3]}. The use of
EKI for the design of training points for the
GP does not require accurate uncertainty quantification
within EKI; it only relies on EKI approximately locating
minimizers of the model-data misfit.
